Question

If the Earth shrinks to 50% of its real radius its mass remaining the same, the weight of a body on the Earth will ______.

Options

• decrease by 50%

• increase by 50%

• decrease by 25%

• increase by 300%

Answer 1

If the Earth shrinks to 50% of its real radius its mass remaining the same, the weight of a body on the Earth will increase by 300%.

g = `"GM"/"R"^2 ⇒ R_1 = 50% "R" = 50/100 xx "R" = 1/2"R"`

`g_1  = "GM"/"R"^2 = "GM"/("R"/2)^2 = "GM"/("R"^2/4) = (4"GM")/"R"^2 = 4g`

∴ g₁ = 4 × g

W = F = mg

W₁ = F₁ = m₁g₁ = m₁g₁

Increase in weight percentage = `("W"_1 - W)/W xx 100`

= `("mg"_1 - "mg")/"mg" xx 100`

= `(4"mg" - "mg")/"mg"`

= 3 × 100

= 300%